Distributed consensus tracking for discrete-time second-order multi-agent systems under asynchronous situation

This paper formulates and solves the asynchronous consensus tracking problem for a discrete-time second-order multi-agent system often used in some physical systems such as robot systems, aircraft systems, and satellite systems. Asynchrony means that each agent's update times, at which the agent updates its state, are determined by its clock that is independent of those of the other agents'. Here we design two asynchronous distributed control protocols, including position control protocol and velocity control protocol. Based on the properties of the product of infinite nonnegative matrices and the composite of binary relation, we derive a sufficient condition to guarantee that the states of all the followers asymptotically converge to the state of the leader. At last a numerical example is presented to demonstrate the validity of the theoretical findings.